# What are the extrema of # f(x)=x/(x-2)# on the interval [-5,5]?

##### 1 Answer

#### Answer:

There are no absolute extrema, and the existence of relative extrema depends on your definition of relative extrema.

#### Explanation:

That is:

So, the function has no absolute maximum on

Now,

This tells us that

Similarly, if your approach allow one-sided relative extrema, then #f(5) is a relative mimimum.

To help visualize, here is a graph. The restricted domain graph is solid and the endpoints are marked.

The natural domain graph extends into the dashed line part of the picture.